AG Mathematische Physik, Christoph Setescak (Regensburg): Disordered Topological Insulators: From Experiment to K-theory

Christoph Setescak (Regensburg)

Disordered Topological Insulators: From Experiment to K-theory

Abstract:
Topological Insulators are semiconductors that exhibit a topological
non-triviality in their mathematical description, leading to the emergence of a
gap-closing surface state at their boundary with certain highly sought-after
properties. Roe C*-algebras provide a mathematical framework to describe
topological insulators in the presence of disorder, whereby the topological
phase corresponds to a non-trivial class in K-theory. It will be illustrated how
atomically resolved experimental data can be reproduced within this framework.
Moreover, these invariants can be calculated numerically via the index of a
Fredholm operator. For the two-dimensional Kane-Mele model we were able to
reproduce the phase diagram previously reported in the literature, but in the
case of the three-dimensional topological insulator Bi2Se3, no result recreating
previous work was obtained.